A clock tower bell sounds to mark off every hour with the number of bells equal to the hour (three consecutive bells sound at three o'clock, etc). The last bell marks the exact beginning of the hour.

The sounding of the bells for six o'clocks starts at 30 seconds before six.

Assuming that the bells are always evenly and equally spaced in time, how long before noon must the sounding of the bells begin?

66 seconds.

This problem is rife with off-by-one errors for the unwary.

In ringing 6 o'clock, there are 5 periods between bells. Since this takes 30 seconds, each period between bells must be 6 seconds long.

In ringing 12 o'clock, there are 11 periods between bells, for a total of 66 seconds.

Posted by Jim Lyon on 2002-07-25 11:41:01